When a two-dimensional source image is projected onto a planar surface, an enlarged version of the image appears on the surface. The projected image will appear as an accurate representation of the source image, albeit at a larger scale, provided that the optical axis of projection is substantially normal to the planar surface. If the same two-dimensional source image is projected normally onto a non-planar surface (or is not projected normally onto a planar surface), however, the projected image will appear distorted.
One way to prevent image distortion when projecting an image onto a non-planar surface is to place a distortion-correcting lens in the optical path. The use of lenses, however, has several drawbacks. First, lenses are expensive. Second, a particular lens may be suitable only for a single surface, making lens use an inflexible solution. Thus, it may not be possible to use a projector having a distortion-correcting lens with multiple different non-planar surfaces if the topographies of the surfaces are very different. Alternatively, it may be necessary to mount the lens or lenses in a manner in which their positions are mechanically adjustable. Mechanically adjusting lens position can be time consuming, and providing an apparatus for mechanically lens adjustment can be expensive.
Another approach for preventing image distortion when projecting a two-dimensional source image onto a non-planar surface involves pre-distorting the image before projecting it. This pre-distortion is sometimes referred to as “warping” the image. This approach requires determining a function that defines the topography of the display surface and determining the inverse of the function. The inverse topographic function is applied to a desired source image in digital form to pre-distort or pre-warp the source image. When the pre-warped source image is projected onto the surface, the warping of the image compensates for the non-planar topography of the surface to produce an image that appears substantially undistorted.
Methods and apparatus for correcting distortion by warping a source image require knowledge of a topographic function suitable for a particular surface. Calibrating a projection system, apparatus, or process may include a variety of procedures, one of which is obtaining the topographic function for the display surface. Known calibration procedures are suitable for applications where the projected image is smaller than the display surface, but may encounter a problem in other applications where it is desired to project the source image out to the outer edges of the display surface. This problem is particularly significant where the shape of the source image and the two-dimensional profile of the display surface when viewed from a front or back side are different.
Accordingly, there is a need for improved systems, methods, and apparatus for calibrating a projector that projects warped images onto a non-planar surface.